Some exact solutions for sediment transport equations. (English) Zbl 1320.86001
Summary: This paper presents some exact solutions for the nonlinear hyperbolic partial differential equations (PDEs), governing sediment transport in channels and rivers. The infinitesimal transformations for the governing system of PDEs are derived by using Lie group analysis. These are used to reduce the number of independent variables and consequently reduces the original system of PDEs into system of ordinary differential equations (ODEs). Moreover, the reduced system of ODEs are solved and new classes of exact group invariant solutions for the governing PDEs are constructed.
MSC:
| 86A05 | Hydrology, hydrography, oceanography |
| 35Q86 | PDEs in connection with geophysics |
| 35A30 | Geometric theory, characteristics, transformations in context of PDEs |
| 35C05 | Solutions to PDEs in closed form |
| 76M60 | Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics |
Keywords:
hyperbolic PDEs; sediment transport; Lie group analysis; infinitesimal transformations; exact solutionReferences:
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